Aptitude - Square Root and Cube Root - Discussion

Guys let me explain this things.
Everyone discuss here is (a-b)^2.

Actually (a-b)^2= (b-a)^2.
For example (5-2)^2=(2-5)^2. Cause square of a negative no is positive.

But you guys know what's wrong in here. The wrong is square root of a no is either positive or negative. In solution taking square root come with +(1-2a) and -(1-2a) so while considering these two we get two answer.

Both of them will satisfy the condition. Hope you guys are get it. Here solution consider only one possibilities of answer.

4*a*a - 4*a + 1 can be written as 4*a*a - 2*a -2*a +1.
Taking 2*a common 2*a(2*a-1)-(2*a - 1).
Hence (2*a-1)(2*a-1).

4*a*a - 4*a + 1 can also be written as 1 + 4*a*a-4*a can be written as 1 + 4*a*a-2*a-2*a.
1 - 2*a + 4*a*a - 2*a.

Taking 1 as common in first two and 2*a in last two then 1(1 - 2*a)-2*a(1 - 2*a).
Hence (1 - 2*a)(1 - 2*a).

So Both Are Correct. So we have to choose any one of these such it satisfies the options available.

@All.

We can take positive or negative square root that is (2a-1) or -(2a-1) => (1-2a) but according to the given option we need a positive value if we consider the value (2a-1) then the answer will be negative.

=> (2a-1)+3a.
=> 5a-1,
=>5*0.1039-1,
=>0.5195-1,
=>-0.4855.

but if we put the value (1-2a) then the calculation will be;
=>(1-2a)+3a.
=>1+a,
=>1+0.1039,
=>1.1039.

Given that a = 0.1039; a<<1; this implies a^2<<<1 and hence it can be ignored int the expression.
So, the value should be approximately equal to 1 - a = 0.8961. The exact value is 0.9393 is also nearly equal to it.

But the option does not contain any matching value. So why should not we consider this question ambiguous?

Hi @Bhavuk Singh.

How told you to take the square root of - .7922?

Actually, when you take the square root of (2a-1) ^2 it will give you two result either 2a-1 else 1-2a.

You can choose any of the two and yes, two results are possible here. Keeping in mind options given you have to select any one of twos. I think this is clear now?

Let me help you guys.

Here the given question can have 2 different answers as;

(1-2a)^2 = 4a^2-4a+1= (2a-1)^2.

Hence for questions like these, try to verify with both the answers and select the given option.
here answers are -0.4805 and 1.1039. so since all options are +ve we select the +ve ans i.e. 1.1039.

Let me explain this. When you solve the the equation under the square root, you can have either (2a - 1) or (1 - 2a). According to the question a = 0.1039.

Hence,
2a-1 = 2* 0.1039 -1 which would be negative. You cannot have a negative number inside the square root though.

Hence we have 1 - 2a.

4 = 2^2 and also 4=(-2)^2.
So sqrt 4 = 2, -2.

So sqrt 4a^2 -4a +1 = +(2a-1),-(2a-1).

So we have choose any one of these such it satisfies the options available.

+(2a-1) + 3a = 5a-1 = -1.5195 such option is not available.

-(2a-1) + 3a = a+1 = 1.1039 this one is option C.

Sq root of 4 is (+ or -) 2.

Because when we do (+ or - 2)^2 in both cases its +4.

Similarly +(1 - 2a)^2 is true and as well as -(1 - 2a)^2 i.e. (2a-1)^2 is also true.

How ever the answer in two cases are different.

So there must be an other answer except option C.

Guys..this will make you understand,
Its 4a^2 * 4a+1... i.e a * 2ab+b^2.where a=2a...(4a^2) and b=1...
So, we got formula of (a-b)^2..removing root..i.e (a-b).

We get,
(2a-1)+3.
(2 * 0.1039- 1) + 3(0.1039).
(0.2078-1) + 0.3117.
0.7922 + 0.31 17.
1.1039.